For the LTI system with the difference equation y[n] = 0.25x[n] +0.5x[n-1] + 0.25x[n-2]
a. Find the impulse response h[n] (this is y[n] when x[n] = δ[n] )
b. Find the frequency response function H(?^?ω). Your result should be in the form of A(?^?θ(?) )[cos(αω)+β]. Specify values for A, ?(?), α,and β
c. Evaluate H(?^?ω) for ω = π , π/2 , π/4, 0, -π/4, - π/2, -π
d. Plot H(?^?ω) in magnitude and phase for –π < ω < π
For the LTI system with the difference equation y[n] = 0.25x[n] +0.5x[n-1] + 0.25x[n-2] a. Find...
(a) Determine the difference equation relating the input (x[n]) and outpt (y[n]) for an LTI system whose impulse response is given by: h(n) = (1/4){δ(n) + δ(n - 1) (b) Find and plot the amplitude and phase response of the above LTI system. Indicate what kind of filter this system represents.
1. A causal LTI system is implemented by the difference equation y(n) = 2r(n) - 0.5 y(n-1). (a) Find the frequency response H/(w) of the system. (b) Plot the pole-zero diagram of the system. Based on the pole zero diagram, roughly sketch the frequency response magnitude |H'(w). (c) Indicate on your sketch of H w , its exact values at w=0, 0.5, and . (d) Find the output signal y(n) produced by the input signal (n) = 3 + cos(0.5...
1. Use the MATLAB command freqz to calculate the DTFT of System 1, to find its frequency response 0.25r[n] + 0.25r|n -2]. H(). For this exercise, System 1 has a different difference equation yn] Find H1 (w) for- aK π, with frequency steps of Δα-π/100. 2. Plot both the magnitude |H1(2)| and the phase LH1(w) vs w, for-π < ώ < π. Use abs and angle commands to obtain magnitude and phase. Label and title both plots and include in...
20. a. Find the system function given the following difference equation: = x (n b. Find the steady-state response to x(n)-cos(π n). C. Find the magnitude and phase of the frequency response for π. ω d. Obtain b from c
20. a. Find the system function given the following difference equation: = x (n b. Find the steady-state response to x(n)-cos(π n). C. Find the magnitude and phase of the frequency response for π. ω d. Obtain b from c
BC:9.4 A LTI discrete time system has an impulse response h[n] =
(−0.6)nu[n] + (0.95)nu[n − 1] Find the transfer function, Hˆ (e jωˆ
), in the normalized frequency domain. Use Matlab to plot the
magnitude and phase (in degrees) of Hˆ (e jωˆ ) in the range of −π
≤ ωˆ ≤ π. Attach your Matlab source code with the plots.
BC:9.4 A LTI discrete time system has an impulse response h[n] = (-0.6)"u[n] + (0.95)"u[n-1] Find the transfer...
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n) as shown in Figure 1, where K 6 (constant), system #1 is described by its impulse response: h(n) = -36(n) + 0.48(n- 1)+8.26(n-2), and system # 2 has the difference equation given by: y(n)+0.1y(n-1)+0.3y(n-2)- 2a(n). (a) Determine the corresponding difference equation of the system #1. Hence, write its fre- quency response. (b) Find the frequency response of system #2. 1 system #1 system #2...
sin(r(n-18/6) r(n-18) n#18 if Consider an LTI discrete-time system that has impulse response h[n] = if otherwise a) Determine the magnitude lH(Q)I and the phase response LH(Q) for-r < Ω < π. Enter Ω as "O" and enter the piecewise function H(S2) using the heaviside function. IH(Q)| = LH(S2) = b) Determine the output of the system, y[n], if the input is given by x[n] = δ[n-71+ cos(쮜. Enter your answer in terms of h[n]. y[n] = In your answers,...
Consider an LTI discrete-time system that has impulse response h n Tn-12) 1 if otherwise a) Determine the magnitude H(Q and the phase response LH(D for-r < Ω < π Enter Ω as "and enter the piecev se function Η Ω using the hea side function b)Determine the output of the system, rn, if the input is given by z n-Sn-9 +com( ) Enter your answer in terms of hin y[n] = In your answers, enter 2(n) for a discrete-time...
Consider an LTI system defined by the difference equationy[n] = -2x[n] + 4x[n-1] - 2x[n-2] (a) Determine the impulse response of this system. (b) Determine the frequency response of this system. Express your answer in the form H(ejw) = A(ejw)e-jwndwhere A(ejw) is a real function of w. Explicitly specify A(ejw) and the delay nd of this system
Consider an LTI system with input sequence x[n] and output sequence y[n] that satisfy the difference equation 3y[n] – 7y[n – 1] + 2y[n – 2] = 3x[n] – 3x[n – 1] (2.1) The fact that sequences x[ ] and y[ ] are in input-output relation and satisfy (2.1) does not yet determine which LTI system. a) We assume each possible input sequence to this system has its Z-transform and that the impulse response of this system also has its Z-transform. Express the...